Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension

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Abstract

We study a nonlinear Dirac system in one space dimension with a quadratic nonlinearity which exhibits null structure in the sense of Klainerman. Using an L-p variant of the L-2 restriction method of Bourgain and Klainerman-Machedon, we prove local well-posedness for initial data in a Sobolev-like space (H-s,H-p) over cap (R) whose scaling dimension is arbitrarily close to the critical scaling dimension.

Original languageEnglish
Pages (from-to)605-616
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series A
Volume20
Issue number3
Publication statusPublished - Mar 2008

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